Out of Hay outofhay.X
The cows have run out of hay, a horrible event that must be remedied
immediately. Bessie intends to visit some of the N (2 <= N <= 2,000)
other farms (numbered 1..N) to survey their hay situation. She'll
traverse some or all of the M (1 <= M <= 10,000) two-way roads whose
length does not exceed 1,000,000,000 that connect the farms. Some
farms may be multiply connected with different length roads.
Bessie is trying to decide how large a waterskin she will need. She knows
that she needs one ounce of water for each unit of length of a road. Since
she can get more water at each farm, she's only concerned about the length
of the longest road. Of course, she plans her route between farms such that
she minimizes the amount of water she must carry.
Help Bessie know the largest amount of water she will ever have to carry:
what is the length of longest road she'll have to travel between any two
farms, presuming she chooses routes that minimize that number?
PROBLEM NAME: outofhay
INPUT FORMAT:
* Line 1: Two space-separated integers, N and M.
* Lines 2..1+M: Line i+1 contains three space-separated integers, A_i,
B_i, and L_i, describing a road from A_i to B_i of length L+i.
SAMPLE INPUT:
3 3
1 2 23
2 3 1000
1 3 43
OUTPUT FORMAT:
* Line 1: A single integer that is the length of the longest road
required to be traversed.
SAMPLE OUTPUT:
43
OUTPUT DETAILS:
In order to reach farm 2, Bessie travels along a road of length 23.
To reach farm 3, Bessie travels along a road of length 43. With
capacity 43, she can travel along these roads provided that she
refills her tank to maximum capacity before she starts down a road.